Best Procedure for Firming Neck and Chin?

It appears from your question that you don't have a lot of sagging of the neck structures (hanging skin, muscle bands, or fat).  If that is true, then the aging changes that you are seeing are most likely the result of diminished elasticity of the skin, which can cause the skin to crepe and wrinkle, giving the skin a 'chicken'  type of appearance. Loss of bone and fat along the jawline and in the chin itself can also contribute to a tired looking neck. 

When there is significant sagging of the neck structures, surgery is almost always the preferred procedure. But in your case it appears that you might benefit from a combination of less invasive procedures. I begin by assessing the need for filler in the chin and along the jawline. Then I look for ways to improve the tone and quality of the skin. I have had good success tightening and improving the skin of the neck and jawline by using a combination of needle-based radiofrequency and fractional ablative laser resurfacing. We do these procedures simultaneously to restore elastin, collagen and hyaluronic acid in the skin while we also improve the surface texture and visible signs of sun-damage. The procedure can be done safely and the results are very satisfying. 

The anatomy of the chin and neck from superficial to deep, includes skin, fat, muscle and deep fascia and bone over the chin.
In younger patients (under 40) who have recessive Chins they may get jowling and loose skin in the neck area. These patients are best managed with Neck Liposuction AND a Chin Implant.
For those above 40 that have jowling, lack neck definition and have loose skin or fatty necks the best procedure is a formal neck lift through a posterior face incision and chin incision. This will enable muscle tightening, fat contouring and skin removal to sharpen the neck.

As we age three things happen we lose the volume, the elasticity and finally the texture. Depending on what area you need defines what approach to take. If you skin only has minor laxity then something such as ulthera or thermage may be a good quick fix. The results of these modalities are modest but are good for maintenance. The best thing is to get an in person/facetime consult with a board certified plastic surgeon. I hope this helps!!